The people supporting the destruction of the masjid believe that Ayodhya is the place of birth of the Hindu god/king Sri Rama, and Babur demolished a temple of Rama and built the Masjid at the place where the temple stood.

Another version of the history is that Babri Masjid was built by Mir Baqi, a Mughalgovernor in 1528, in the honor of Babur and the people who support it argue that there is no account of destruction of any Hindutemple or association of Rama with the site in MedievalIndian literature.They claim that nowhere in any of the popular versions of the Ramayana, the place of birth of Rama is mentioned as the place where the Masjid was located.

There had been disputes regarding the Masjid for centuries.
In A.D. 1788, Jesuit priest Joseph Tieffenthaler suggested that the birth of Rama is believed to be in the vicinity of the Masjid.

In December 1949, a statute of Sri Rama appeared in the Mosque at night. The Hindus believed it to be a miracle and the Masjid was declared by the District Magistrate as a disputed property and was closed to the Muslims.

On November 6, 1986, foundation stones were laid(Shilanyas) for building a Hindu temple in Ayodhya.

In spite of the repeated negotiations between the two sides, the dispute over the Masjid was intensified in the years to come.

How the Masjid was destroyed:

Bharatiya Janata Party, Vishva Hindu Parishad, and RSS decided for Kar Seva(Action Service), and more than 300,000 volunteers gathered for the Kar Seva. Police did not intervene much because of the political pressures. Babri Masjid, was broken down to bricks within a few hours. The Kar Sevaks were prepared to start the construction of the temple as soon as possible. Half an hour after the mosque had been stormed, water began to be pumped into a small, crude, tank-like, brick-and-mud structure a little distance away from the mosque. This was to mix the cement that was later used to build the platform and wall of the temple on the rubble of the mosque.

After December 6:

The rule of the Central Government was imposed in Uttar Pradesh at 6 p.m. on December 6. During the following week, communal riots spread throughout the countryside, killing around 1,700 people. Riots broke out again in Bombay from January 9 through January 11, killing 500 more people. In March 1993, the BombayStock Exchange and other prominent places in the city were shaken by bomb blasts. This was followed by a number of riots in different parts of India.